Question

Частица массой m, несущая заряд q, движется в однородном магнитном поле с индукцией B по окружности радиусом R со скоростью u. Что произойдет с радиусом орбиты, периодом обращения и импульсом частицы при увеличении заряда частицы?

Answer 1

Радиус орбиты уменьшится 
$F=Bqv$   $F=ma= \frac{m v^{2} }{R}$
$\frac{m v^{2} }{R} = Bqv$
$R = \frac{mv}{Bq}$
Период обращения уменьшится
$T= \frac{2 \pi R}{v} = \frac{2 \pi m}{Bq}$
Импульс частицы не изменится так как сила Лоренца зависит от скорости, а не наоборот.

Answer 2

Particle Motion in a Magnetic Field

When a particle with mass m and charge q moves in a uniform magnetic field with induction B along a circular path of radius R at a speed u, several aspects of its motion are affected. Let's explore how the radius of the orbit, the period of revolution, and the momentum of the particle change as the charge of the particle is increased.

Radius of Orbit

As the charge of the particle is increased, the radius of the orbit will be affected. The radius of the orbit is given by the equation:

R = (m * u) / (q * B)

This equation shows that the radius of the orbit is inversely proportional to the charge of the particle. Therefore, as the charge of the particle is increased, the radius of the orbit will decrease.

Period of Revolution

The period of revolution, which is the time taken for the particle to complete one full revolution along its circular path, is also influenced by the charge of the particle. The period of revolution is given by the equation:

T = (2 * π * m) / (q * B)

Similar to the radius of the orbit, the period of revolution is inversely proportional to the charge of the particle. Hence,